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Connected sums of knots do not admit purely cosmetic surgeries
Published 11 Sep 2019 in math.GT | (1909.05048v1)
Abstract: Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in $S3$ do not admit purely cosmetic surgeries. In this article, we confirm this conjecture for connected sums of knots by analysing the JSJ-structures.
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